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Sagot :
CORRELATIONS
Answer:
1. Correlation coefficients measure the strength of a linear relationship between two variables, x and y. A positive link is shown by a linear correlation coefficient larger than zero. A number less than zero indicates a negative association. Finally, a value of 0 shows that there is no link between x and y.
The correlation coefficient () is a metric that measures how closely two variables' movements are related. The Pearson product-moment correlation, which generates the most frequent correlation coefficient, is used to quantify the linear connection between two variables. This correlation coefficient, however, may not always be an acceptable measure of reliance in a non-linear connection.
When the correlation coefficient is larger than zero, it indicates that both variables are moving in the same direction. When is +1, it means that the two variables being compared have a complete positive association; when one variable goes higher or lower, the other variable moves in the same direction and magnitude. The stronger the linear correlation, the closer the value of is to +1. Assume, for example, that the price of an airline ticket is directly tied to the price of oil, with a correlation coefficient of +0.95. The association between oil prices and airfares is very strong positive, with a value close to +1. As a result, as the price of oil falls, so do airfares, and as the price of oil rises, so do airfares.
When the correlation coefficient is less than zero, we have a negative (inverse) correlation. This indicates that two variables are moving in opposite directions. In a nutshell, any value between 0 and -1 indicates that the two securities are moving in opposing directions. The connection is said to be totally negatively linked when is -1. In other words, if one variable grows, the other variable reduces by the same amount (and vice versa). The degree to which two securities are adversely connected, on the other hand, may fluctuate over time (and they are almost never exactly correlated all the time).
2. There is no simple method to express how changes in the values of the independent variable impact the values of the dependent variable in a non-linear relationship.
When two variables have no discernible link, they are said to be unconnected, or to have a null relationship. Variable value changes are caused by random occurrences, not by the impact of one on the other.
To demonstrate a causal link between two variables, four requirements must be met:
1) Time order: the cause must exist prior to the effect.
2) Covariation: a change in the cause results in a change in the effect.
3) Rationale: There must be a logical explanation for why they are connected.
4) non-spuriousness: there is no alternative (rival) explanation for the effect.
Nonlinearity is a statistical word that refers to a scenario in which there is no straight-line or direct link between an independent variable and a dependent one. Changes in the output do not vary in direct proportion to changes in any of the inputs in a nonlinear connection. When studying cause and effect relationships, nonlinearity is a prevalent problem. In such cases, extensive modeling and hypothesis testing are required to provide explanations for nonlinear phenomena. Nonlinearity without explanation might result in unpredictable and irregular results.
Nonlinearity in investing can be seen in specific investment classes. Changes in the input variables linked with options, for example, are nonlinear derivatives since they do not result in proportionate changes in output. Investments with a high degree of nonlinearity may arise more frequently.
What is the relationship between linear and Non linear text
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